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Under ergodic condition, the analytic expressions for the fluctuations of temperature and particle number in the well of a system are obtained rigorously in particle-spilling-from-well model by means of integration approaches in phase space; the relationships among fluctuations of thermodynamic variables, the total particle numbers, and the well volume are emphasized. Results show that the less the total number of particles and the smaller the well's volume, the more remarkable the thermodynamic fluctuations effect, and the more closely the thermodynamic fluctuations related to the particle spilling from the well. There is a one to one correspondence between particle spilling from the well and the occurrence of negative specific heat, and the huge thermodynamic fluctuations,as well as, the origin of this phenomenon can be understood by the apparent energy inverse partition.
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Keywords:
- particle-spilling-from-single potential well model /
- fluctuation /
- apparent energy inverse partition /
- negative specific heat
[1] Feng D L, Feng Y H, Zhang X X 2013 Acta Phys. Sin. 62 083602(in Chinese) [冯黛丽, 冯妍卉, 张欣欣 2013 62 083602]
[2] Xiao X Y 2012 Chin Phys. B 21 046102
[3] Zhang L, Wang S Q, Chen N X 2012 Chin Phys.B 21 033601
[4] Shao C W, Wang Z H, Li Y N, Zhao Q, Zhang L 2013 Acta Phys. Sin. 62 083602(in Chinese) [邵琛玮, 王振华, 李艳男, 赵骞, 张林 2013 62 083602]
[5] Zhang L, Li W, Sun H X, Zhang C B, Xu S N 2009 Acta Phys. Sin. 58 58(in Chinese) [张林, 徐送宁, 李蔚, 孙海霞, 张彩碚 2009 58 58]
[6] Wu Z M, Wang X Q, Yang Y Y 2007 Chin Phys. 16 405
[7] Pochodzalla J 1995 Phys. Rev. Lett. 75 1040
[8] Ma Y G, Siwek A, Péter J, Gulminelli, F, Dayras, R, Nalpas L, Tamain B, Vient E, Auger G, Bacri CO, Benlliure J, Bisquer E, Borderie B, Bougault R, Brou R, Charvet J L, Chbihi A, Colin J, Cussol D, DeFilippo E, Demeyer A, Dore D, Durand D, Ecomard P, Eudes P, Gerlic E, Gourio D, Guinet D, Lautesse P, Laville J L, Lebreton L, Lecolley J F, Le Fevre A, Lefort T, Legrain R, Lopez O, Louvel M, Lukasik J, Marie N, Metivier V, Ouatizerga A, Parlog M Plagnol E, Rahmani A, Reposeur T, Rivet MF, Rosato E, Saint-Laurent F, Squalli M, Steckmeyer J C, Stern M, Tassan-Got L, Volant C, Wieleczko P J 1997 Phys. Lett. B 390 41
[9] D’Agostino M, Botvina A S, Bruno M, Bonasera A Bondorf J P, Bougault R, Desquerelles P, Geraci E, Gulminelli F, Iori I, Le N Neindre, G. VMargagliotti, Mishustin N, Moroni A, Pagano A, Vannini G. 1999 Nucl. Phys. A 650 329
[10] Schmidt M, Kusche R, Kronmller W, Von Issendorff B, Haberland H 1997 Phys. Rev. Lett. 79 99
[11] Chomaz P, Gulminelli F 1999 Nucl. Phys. A 647 153
[12] Bachels T, Gntherodt H J, Schäfer R 2000 Phys. Rev. Lett. 85 1250
[13] Kofman R, Cheyssac P, Celestini F 2001 Phys. Rev. Lett. 86 1388
[14] Schmidt M, Hippler T, Donges J, Schmidt M., Hippler T, Donges J, Kronmller W, Von Issendorff B, Haberland H., Labastie P 2001 Phys. Rev. Lett. 87 203402
[15] Gobet F, Farizon B, Farizon M, Gaillard M J, Miark T D 2001 Phys. Rev. Lett. 87 203401
[16] Gobet F, Farizon B, Farizon M, Gaillard M J, Buchet J P, Carré M, Scheier P, Märk T D 2002 Phys. Rev. Lett. 89 183403
[17] Bréchignac C, Cahuzac P, Concina B, Leygnier J 2002 Phys. Rev. Lett. 89 203401
[18] Breaux G A, Benirschke R C, Sugai T, Kinnear B S, Jarrold M F 2003 Phys. Rev. Lett. 91 215508
[19] Schmidt M, Kusche R, Hippler T, Donges J, Kronmller W, Von Issendorff B, Haberland H 2001 Phys. Rev. Lett. 86 1191
[20] Leviatan A, Ginocchio J N 2003 Phys. Rev. Lett. 90 212501
[21] Behringer H, Pleimling M, Huller A 2005 J. Phys. A 38 973
[22] Casetti L, Kastner M 2006 Phys. Rev. Lett. 97 100602
[23] Ramírez-Hernández A, Larralde H, Leyvraz F 2008 Phys. Rev. Lett. 100 120601
[24] Ramírez-Hernández A, Larralde H, Leyvraz F 2008 Phys. Rev. E 78 061133
[25] Michaelian K, Santamaría-Holek I, Pérez-Madrid A 2009 Phys. Rev. Lett. 102 138901
[26] Andersen T D, Lim C C 2007 Phys. Rev. Lett. 99 165001
[27] Carignano M A, Gladich I 2010 Europhys. Lett. 90 63001
[28] Staniscia F, Turchi A, Fanelli D, Chavanis P H, and De Ninno G 2010 Phys. Rev. Lett. 105 010601
[29] Campisi M, Zhan F, Hänggi P 2012 Europhys. Lett. 99 60004
[30] Thirring W, Narnhofer H 2003 Phys. Rev. Lett. 91 130601
[31] Rao J, Liu Q H, Liu T G, Li L X 2008 Ann. Phys. 323 1415
[32] Pathria R K, Beale Paul D 2012 Statistical Mechanics (Singapore: Elsevier) p584-587
[33] Shen Y H, Liang Z Z, Cai L H, Cai Q Q 2004 Practical mathematical Manual (Beijing: Science Press) p207-208 (in Chinese) [沈永欢, 梁在中, 蔡履瑚, 蔡蒨蒨 2004 实用数学手册 (北京: 科学出版社) 第207–208页]
[34] Feitosa K, Menon N 2002 Phys. Rev. Lett. 88 198301
[35] Götzendorfer A, Kreft J, Kruelle C A, Rehberg I 2005 Phys. Rev. Lett. 95 135704
[36] Watanabe K, Tanaka H 2008 Phys. Rev. Lett. 100 158002
[37] Wang H Q, Menon N 2008 Phys. Rev. Lett. 100 158001
[38] Hou M, Tu H, Liu R, Li Y, Lu K, Lai P Y, Chan C K 2008 Phys. Rev. Lett. 100 068001
[39] Rivas N, Ponce S, Gallet B, Risso D, Soto R, Cordero P, Mujica N 2011 Phys. Rev. Lett. 106 088011
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[1] Feng D L, Feng Y H, Zhang X X 2013 Acta Phys. Sin. 62 083602(in Chinese) [冯黛丽, 冯妍卉, 张欣欣 2013 62 083602]
[2] Xiao X Y 2012 Chin Phys. B 21 046102
[3] Zhang L, Wang S Q, Chen N X 2012 Chin Phys.B 21 033601
[4] Shao C W, Wang Z H, Li Y N, Zhao Q, Zhang L 2013 Acta Phys. Sin. 62 083602(in Chinese) [邵琛玮, 王振华, 李艳男, 赵骞, 张林 2013 62 083602]
[5] Zhang L, Li W, Sun H X, Zhang C B, Xu S N 2009 Acta Phys. Sin. 58 58(in Chinese) [张林, 徐送宁, 李蔚, 孙海霞, 张彩碚 2009 58 58]
[6] Wu Z M, Wang X Q, Yang Y Y 2007 Chin Phys. 16 405
[7] Pochodzalla J 1995 Phys. Rev. Lett. 75 1040
[8] Ma Y G, Siwek A, Péter J, Gulminelli, F, Dayras, R, Nalpas L, Tamain B, Vient E, Auger G, Bacri CO, Benlliure J, Bisquer E, Borderie B, Bougault R, Brou R, Charvet J L, Chbihi A, Colin J, Cussol D, DeFilippo E, Demeyer A, Dore D, Durand D, Ecomard P, Eudes P, Gerlic E, Gourio D, Guinet D, Lautesse P, Laville J L, Lebreton L, Lecolley J F, Le Fevre A, Lefort T, Legrain R, Lopez O, Louvel M, Lukasik J, Marie N, Metivier V, Ouatizerga A, Parlog M Plagnol E, Rahmani A, Reposeur T, Rivet MF, Rosato E, Saint-Laurent F, Squalli M, Steckmeyer J C, Stern M, Tassan-Got L, Volant C, Wieleczko P J 1997 Phys. Lett. B 390 41
[9] D’Agostino M, Botvina A S, Bruno M, Bonasera A Bondorf J P, Bougault R, Desquerelles P, Geraci E, Gulminelli F, Iori I, Le N Neindre, G. VMargagliotti, Mishustin N, Moroni A, Pagano A, Vannini G. 1999 Nucl. Phys. A 650 329
[10] Schmidt M, Kusche R, Kronmller W, Von Issendorff B, Haberland H 1997 Phys. Rev. Lett. 79 99
[11] Chomaz P, Gulminelli F 1999 Nucl. Phys. A 647 153
[12] Bachels T, Gntherodt H J, Schäfer R 2000 Phys. Rev. Lett. 85 1250
[13] Kofman R, Cheyssac P, Celestini F 2001 Phys. Rev. Lett. 86 1388
[14] Schmidt M, Hippler T, Donges J, Schmidt M., Hippler T, Donges J, Kronmller W, Von Issendorff B, Haberland H., Labastie P 2001 Phys. Rev. Lett. 87 203402
[15] Gobet F, Farizon B, Farizon M, Gaillard M J, Miark T D 2001 Phys. Rev. Lett. 87 203401
[16] Gobet F, Farizon B, Farizon M, Gaillard M J, Buchet J P, Carré M, Scheier P, Märk T D 2002 Phys. Rev. Lett. 89 183403
[17] Bréchignac C, Cahuzac P, Concina B, Leygnier J 2002 Phys. Rev. Lett. 89 203401
[18] Breaux G A, Benirschke R C, Sugai T, Kinnear B S, Jarrold M F 2003 Phys. Rev. Lett. 91 215508
[19] Schmidt M, Kusche R, Hippler T, Donges J, Kronmller W, Von Issendorff B, Haberland H 2001 Phys. Rev. Lett. 86 1191
[20] Leviatan A, Ginocchio J N 2003 Phys. Rev. Lett. 90 212501
[21] Behringer H, Pleimling M, Huller A 2005 J. Phys. A 38 973
[22] Casetti L, Kastner M 2006 Phys. Rev. Lett. 97 100602
[23] Ramírez-Hernández A, Larralde H, Leyvraz F 2008 Phys. Rev. Lett. 100 120601
[24] Ramírez-Hernández A, Larralde H, Leyvraz F 2008 Phys. Rev. E 78 061133
[25] Michaelian K, Santamaría-Holek I, Pérez-Madrid A 2009 Phys. Rev. Lett. 102 138901
[26] Andersen T D, Lim C C 2007 Phys. Rev. Lett. 99 165001
[27] Carignano M A, Gladich I 2010 Europhys. Lett. 90 63001
[28] Staniscia F, Turchi A, Fanelli D, Chavanis P H, and De Ninno G 2010 Phys. Rev. Lett. 105 010601
[29] Campisi M, Zhan F, Hänggi P 2012 Europhys. Lett. 99 60004
[30] Thirring W, Narnhofer H 2003 Phys. Rev. Lett. 91 130601
[31] Rao J, Liu Q H, Liu T G, Li L X 2008 Ann. Phys. 323 1415
[32] Pathria R K, Beale Paul D 2012 Statistical Mechanics (Singapore: Elsevier) p584-587
[33] Shen Y H, Liang Z Z, Cai L H, Cai Q Q 2004 Practical mathematical Manual (Beijing: Science Press) p207-208 (in Chinese) [沈永欢, 梁在中, 蔡履瑚, 蔡蒨蒨 2004 实用数学手册 (北京: 科学出版社) 第207–208页]
[34] Feitosa K, Menon N 2002 Phys. Rev. Lett. 88 198301
[35] Götzendorfer A, Kreft J, Kruelle C A, Rehberg I 2005 Phys. Rev. Lett. 95 135704
[36] Watanabe K, Tanaka H 2008 Phys. Rev. Lett. 100 158002
[37] Wang H Q, Menon N 2008 Phys. Rev. Lett. 100 158001
[38] Hou M, Tu H, Liu R, Li Y, Lu K, Lai P Y, Chan C K 2008 Phys. Rev. Lett. 100 068001
[39] Rivas N, Ponce S, Gallet B, Risso D, Soto R, Cordero P, Mujica N 2011 Phys. Rev. Lett. 106 088011
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